Since the Lipschitz properties of convolutional neural network (CNN) are widely considered to be related to adversarial robustness, we theoretically characterize the 1 norm and ∞ norm of 2D multi-channel convolutional layers and provide efficient methods to compute the exact 1 norm and ∞ norm. Based on our theorem, we propose a novel regularization method termed norm decay, which can effectively reduce the norms of CNN layers. Experiments show that normregularization methods, including norm decay, weight decay, and singular value clipping, can improve generalization of CNNs. However, we are surprised to find that they can slightly hurt adversarial robustness. Furthermore, we compute the norms of layers in the CNNs trained with three different adversarial training frameworks and find that adversarially robust CNNs have comparable or even larger norms than their nonadversarially robust counterparts. Moreover, we prove that under a mild assumption, adversarially robust classifiers can be achieved with neural networks and an adversarially robust neural network can have arbitrarily large Lipschitz constant. For these reasons, enforcing small norms of CNN layers may be neither effective nor necessary in achieving adversarial robustness. Our code is available at https://github.com/ youweiliang/norm_robustness.
In this paper, a novel protein remote homology detection algorithm based on multiple heterogeneous biological features and kernel affinity propagation clustering is proposed. The kernel method is used to integrate the heterogeneous data sources related to protein remote homolog. In addition prediction accuracy method is extended to validate our proposed algorithm.
Since the Lipschitz properties of convolutional neural networks (CNNs) are widely considered to be related to adversarial robustness, we theoretically characterize the L-1 norm and L-infinity norm of 2D multi-channel convolutional layers and provide efficient methods to compute the exact L-1 norm and L-infinity norm. Based on our theorem, we propose a novel regularization method termed norm decay, which can effectively reduce the norms of convolutional layers and fully-connected layers. Experiments show that norm-regularization methods, including norm decay, weight decay, and singular value clipping, can improve generalization of CNNs. However, they can slightly hurt adversarial robustness. Observing this unexpected phenomenon, we compute the norms of layers in the CNNs trained with three different adversarial training frameworks and surprisingly find that adversarially robust CNNs have comparable or even larger layer norms than their non-adversarially robust counterparts. Furthermore, we prove that under a mild assumption, adversarially robust classifiers can be achieved using neural networks, and an adversarially robust neural network can have an arbitrarily large Lipschitz constant. For this reason, enforcing small norms on CNN layers may be neither necessary nor effective in achieving adversarial robustness. The code is available at https://github.com/youweiliang/norm_robustness.
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